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The set {a, b, c} has exactly eight subsets.
- List all the subsets of {a, b, c}.
- Now arrange those subsets in a sequence so that each subset in the
sequence differs from the one before it in one of two ways:
- One new element is inserted:
Example 1: {a}, {a, b}
Example 2: {a, b}, {a, b, c}
- One old element removed
Example 1: {a, b, c}, {a, c}
Example 2: {b}, Ø
- Can you create more than one sequence that fits these criteria?
- Create a listing like this for the subsets of {a, b, c, d}.
- Describe a general method (or explain why there isn’t one) for creating such a
sequence of the subsets of any set {a1, a2, a3, ...an}.
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